Answer:
[tex]x = n\pi + ( { - 1)}^{n} \times \frac{3\pi}{2} [/tex]
Step-by-step explanation:
We want to find the x-intercepts of
[tex]y = \sin(x) + 1[/tex]
At x-intercept, y=0.
[tex]0 = \sin(x) + 1[/tex]
[tex] \sin(x) = - 1[/tex]
Take sine inverse of both sides to get:
[tex]x = { \sin }^{ - 1} ( - 1)[/tex]
[tex]x = n\pi + ( { - 1)}^{n} { \sin }^{ - 1} ( 1)[/tex]
The x-intercepts are:
[tex]x = n\pi + ( { - 1)}^{n} \times \frac{3\pi}{2} [/tex]
for n being an integer
